Credit Market Problems January 2011 () Credit Markets January - - PowerPoint PPT Presentation

Credit Market Problems

January 2011

() Credit Markets January 2011 1 / 17

Should Governments Intervene in Credit Markets

Moneylenders historically viewed as exploitive: high interest rates , ! BUT displacing them may remove valuable/unique services , ! and interest rates may re‡ect high costs (Aleem, 1990 and Steel et. al. 1997) Two main rationales for intervention , ! E¢ciency: are productive investments not being undertaken? , ! Distribution: is access to credit equitable? , ! there need not be a trade-o¤

() Credit Markets January 2011 2 / 17

Agency Problems

Reasons for absence of formal institutions in village economies A result of limited liability (lack of collateral) and asymmetric information Even when titled land is available, formal banks may not accept it as collateral

() Credit Markets January 2011 3 / 17

Adverse Selection

Example Investment requires $1, but borrowers have no wealth A fraction q of borrowers are “safe”: earn certain output y A fraction 1 q of borrowers are “risky”: Output = ¯ y with probability p with probability 1 p Bank cannot distinguish borrower types Equal expected return: p ¯ y =y. Gross cost to bank per $1 lent = k, where y > k Bank charges gross (interest plus principle) lending rate = R

() Credit Markets January 2011 4 / 17

How does the bank’s expected pro…t vary with R?

Given R, the bank’s expected return per dollar lent is [q + (1 q)p] R De…ne the “break-even” value of R as Rb [q + (1 q)p] Rb = k Rb = k q + (1 q)p Rb = k + (1 q)(1 p)k q + (1 q)p Rb = k + A Bank’s expected pro…t: ¯ π = [q + (1 q)p] R k if R < y pR k if R > y

() Credit Markets January 2011 5 / 17

π

R k k+A y k/p y/p

() Credit Markets January 2011 6 / 17

π

R k k+A y k/p y/p

() Credit Markets January 2011 7 / 17

Implications

Raising interest rates need not increase pro…ts linearly If p falls, the bank may not be able to break even at a rate low enough for safe borrowers ) Banks will only serve risky borrowers , ! this is ine¢cient (since y > k) and inequitable , ! credit rationing

() Credit Markets January 2011 8 / 17

Moral Hazard

Example (Ghosh, Mookherjee and Ray 2000) Indivisible project requires funds L All agents risk neutral Likelihood of high output depend on non-contractible e¤ort e : Output = Q if good harvest with prob. p(e) if crop failure with prob. 1 p(e) where p0(e) > 0 , p00(e) < 0

() Credit Markets January 2011 9 / 17

Case 1: Self–…nanced farmer (benchmark)

Farmer chooses e to solve max

e

p(e).Q e L , ! FOC p0(e) = 1 Q where e = …rst–best (e¢cient) e¤ort level

() Credit Markets January 2011 10 / 17

Case 2: Debt–…nanced farmer

Total debt: R = (1 + i)L Limited Liability: In case of default can only lose collateral, w < L Farmer chooses e to solve max

e

p(e).(Q R) + (1 p(e)).(w) e , ! FOC yields the incentive curve: p0(ˆ e) = 1 Q + w R (IC) , ! ˆ e(w, R) is decreasing in R and increasing in w , ! if R > L > w, it follows that ˆ e < e

() Credit Markets January 2011 11 / 17

Lender’s pro…t: π = p(e)R + [1 p(e)] w L Competitive lending (Figure 1) ) π = 0 : R = L w p(e) + w = L (1 p(e))w p(e) (ZP) , ! equilibrium: determined by intersection of (IC) and (ZP) Monopoly lending ) maximize pro…ts subject to IC (Figure 2) , ! if max pro…t is πM then isopro…t line is R = L πM (1 p(e))w p(e) (MP)

() Credit Markets January 2011 12 / 17

Isoprofit Curve Incentive Curve R R ^ e e* e ^ E

Figure 1: Equilibrium Debt and Effort in the Credit Market. the lender’s market power (although that certainly exacerbates the problem), but

Isoprofit Curve Incentive Curve R R ^ e e* e ^ E E'

Figure 2: Effect of an Increase in the Lender’s Profit. The observation that borrower-friendly equilibria are more efficient has broad

An increase in collateral, w (Figure 3) , ! fall in the equilibrium interest rate and debt, and an increase in the e¤ort level. , ! for a …xed π, the borrower’s income increases ) interest rate dispersion, even in competitive credit markets ) exaccerbates pre-existing inequality

() Credit Markets January 2011 13 / 17

R e E' E

Isoprofit Curve Incentive Curve

Figure 3: Effect of Higher Borrower Wealth (Collateral).

Enforcement Problems (Ex Post Moral Hazard)

Example (Ghosh, Mookherjee and Ray 2000) In…nite horizon lending–borrowing game with no saving and discount factor δ Borrower’s production technology is F(L) where F 0(L) > 0 and F 00(L) < 0 r = bank rate of interest (opportunity cost of funds) Self–…nanced farmer (benchmark): max

L

F(L) (1 + r)L , ! FOC: F 0(L) = 1 + r

() Credit Markets January 2011 14 / 17

Partial Equilibrium: Single Lender

Assume that a defaulting borrower goes into “autarky” and receives v (exogenous for now) Borrower’s incentive constraint: F(L) + δ 1 δv 1 1 δ [F(L) R] (IC) Optimal contract solves max

L,R

F(L) R subject to R

• δ [F(L) v]

(IC) z = R (1 + r)L (PC) where z is lender’s minimum pro…t

() Credit Markets January 2011 15 / 17

Two types of solution: (1) if indi¤erence curves are tangent to isopro…t curve between A and B at L, this is the solution and IC is not binding (2) if not, both constraints are binding and solution ˆ L(v, z) is at corner B , ! in general, the constrained optimal level of lending is ˜ L(v, z) = min

• L, ˆ

L(v, z)

• ()

Credit Markets January 2011 16 / 17

R L R

~

L

~

L*

Borrower's indifference curve Incentive constraint Isoprofit line

A B Figure 4: Optimal Solution to the Enforcement Problem. subject to the constraints

Some Implications

Increase in lender’s pro…t z ! PC shifts up (Figure 5) , ! reduced lending, L , ! increase in interest rate, R/L Increase in value of outside option, v ! IC shifts down (Figure 6) , ! reduced lending, L , ! increase in interest rate, R/L Can credit rationing arise in equilibrium ? , ! yes: if z or v become high enough there is no combination of L and R that satis…es both (IC) and (PC)

() Credit Markets January 2011 17 / 17

R L

Incentive constraint Isoprofit line

Figure 5: Effect of an Increase in Lender’s Profit. leads to the conclusion:

R L Incentive Constraint Isoprofit Line B B'

Figure 6: Effect of an Increase in Borrower’s Outside Option.